Note that this assumption is looser than the one in [1]}.
We denote by \(\Vert A\Vert \)  the matrix norm
\(\Vert A\Vert =\sup _{u \ne 0, v \ne 0}\frac{\langle v, Au\rangle }{\Vert v\Vert _\mathrm {d}\Vert u\Vert _\mathrm {p}}= \sup _{u\ne 0} \frac{\Vert Au\Vert _{\mathrm {d},*}}{\Vert u\Vert _\mathrm {p}}= \sup _{v\ne 0} \frac{\Vert A^Tv\Vert _{\mathrm {p},*}}{\Vert v\Vert _\mathrm {d}},\) 
